Line Srucure-based Localizaion for Soccer Robos Hannes Schulz, Weichao Liu, Jörg Sückler, Sven Behnke Universiy of Bonn, Insiue for Compuer Science VI, Auonomous Inelligen Sysems, Römersr. 164, 53117 Bonn, Germany {schulz,liu,sueckler,behnke}@ais.uni-bonn.de Absrac The rules in RoboCup soccer more and more discourage a solely color-based orienaion on he soccer field. While he field size increases, field boundary markers and goals become smaller and less colorful. For robus game play, robos herefore need o mainain a sae and rely on more suble environmenal clues. Field lines are paricularly ineresing, because hey are hardly compleely occluded and observing hem significanly reduces he number of possible poses on he field. In his work we presen a mehod for line-based localizaion. Unlike previous work, our mehod firs recovers a line srucure graph from he image. From he graph we can hen easily derive feaures such as lines and corners. Finally, we describe opimizaions for efficien use of he derived feaures in a paricle filer. The mehod described in his paper is used regularly on our NimbRo humanoid soccer robos. I. INTRODUCTION On is way o realisic soccer environmens, RoboCup sared ou wih small-sized, color-coded scenarios. Gradually, arificial markers, colors and special lighing are removed and he soccer field size increases o encourage eams o build reliable vision sysems which can compee under realworld condiions. While oher leagues, like he MidSize league, already wen a long way, he humanoid league is sill a he beginning of his ransiion. Especially he small available compuaional power and noisy observaions due o mosly unmodelled moion models prevened large seps so far. However, from he experience in MidSize-league we can learn ha he removal of colored landmarks emphasizes he imporance of field lines. For precise posiioning, for example during seup phase of he game, use of lines and crossings is already mandaory since he uncerainies of oher landmarks are prohibiively large. In his work we presen a sysem for deecing field-lines and employing hem for localizaion. This is by far no he firs mehod presened for he purpose; however, our approach has several advanages. The line srucure is deermined using algorihms inspired from previous work on analysis of handwrien digis [1]. This mehod employs local and global cues o deermine a graph which capures he essenial srucure of lines in an image aken by he robo s camera. The graph has a paricularly nice srucure: nodes are candidaes for corners where he field lines mee wih he branching facor deermining he corner ype. Edges in he graph correspond o Fig. 1. Localizaion using line and corner feaures. The op-figure shows an image aken from he robo s fron camera. The purple line denoes he deeced field boundary, red green lines show field lines no used for localizaion. Deeced corners are marked as X or T. Boom lef: egocenric view wih everyhing used for localizaion. Boom righ: resuling localizaion using he paricle filer. field lines. Mos imporanly, he esimaes of line parameers are no influenced by spurious segmens or noisy locally esimaed orienaions. Noably, he favorable properies of he algorihm come a lile cos. We incorporaed line and corner feaures ino a paricle filer which runs online on our NimbRo humanoid soccer robos. This is possible, because he cosly per-paricle associaion decision of observed feaures o landmarks can be simplified. The remainder of he paper is organized as follows. The nex secion reviews previous work on line-based localizaion. Secion III and IV describe preprocessing and feaure exracion, respecively. In Secion V we describe how line and corner feaures can be used in a paricle filer. We provide Proceedings of he 4h Workshop on Humanoid Soccer Robos A workshop of he 009 IEEE-RAS Inl. Conf. On Humanoid Robos Humanoids 009, ParisFrance, 009, December 7-10
qualiaive and quaniaive experimenal resuls in Secion VI. II. RELATED WORK Work on field-lines for localizaion in RoboCup environmens can be described on hree axes. Firs, how candidae line segmens are found; second, how he line segmens are merged o lines; and hird, how deeced lines are used for localizaion. Naurally, he lieraure describes only combinaions of all hree approaches and his work is no excepion. Neverheless, his work conribues o all hree areas. Finding candidae line segmens is usually performed using green-whie-green ransiion filers [] or scan-lines [3], [4] on he image. However, convolving he image is an expensive operaion and scan-lines ignore conex. Our mehod simply makes use of all whie pixels and rejecs hose which are no par of he field lines. Candidae line segmens are hen processed o find acual lines. Hough-space echniques are commonly used for his purpose e.g. [5], [6]. These mehods need o calculae a large accumulaor array and require double book-keeping of linepieces for pos-processing he found lines. Also, esimaed line orienaions of small segmens end o be quie noisy. The same is rue for he approach followed by he NAO eam NUManoid [], where lines are deermined by adding and removing poins o candidae lines which requires uning of numerous parameers. In he approach presened here, candidaes for lines emerge naurally from he deermined line srucure graph. Finally, candidae line segmens or lines can be used for localizaion. Lauer e. al. [7] use all candidae line segmens for performing a gradien descen from he currenly esimaed pose. This echnique relies on he favorable properies of omnidirecional cameras, which are no allowed in he humanoid league, and on sable disance esimaes, which are hard o deermine for humanoid robos wih unknown camera pich and roll angles. Röfer e. al. [4] also make use of all candidae line segmens using a pre-calculaed lookup able for he observaion model. Wih his mehod, segmens which are observed on a line can be associaed wih differen lines in he world, supporing improbable poses. In our experience, his approach also requires a large floor and sandard deviaions in he observaion model such ha spurious line segmens do no compleely desroy he belief. For precise localizaion, his approach is no helpful. Furhermore, he compuaional load is high if i s used in combinaion wih paricle filers, where each paricle has o inegrae informaion from all candidae line segmens. Consequenly, in humanoid and AIBO eams, field line exracion from candidae line segmens prevails for localizaion purposes. The resuling long lines can hen eiher be used as pose consrains [8] or direcly used in a paricle filer. Pose consrains rule ou many possible poses and need o be relaxed ieraively in he case where no allowed poses are lef. Paricle filers can represen much more complex beliefs. However, o achieve real-ime performance, speed opimizaion is criical. In his work, we describe opimizaions used o acquire a high frame-rae even when many feaures are deeced in an image. III. VECTORIZATION The firs sep of our algorihm is he vecorizaion of he field lines. Our robos are equipped wih hree color cameras IDS ueye 16 LE which capure images wih a WXGA 75 480 resoluion in YUV 4:: color space. The individual pixels are classified o color classes as follows. Firs, he Y-componen is compared o luminance hresholds for classificaion of black and whie. For pixels wih inermediae luminance, he color class is defined by a lookup-able for he U and V values. Color classes are described by ellipses in he UV plane. In addiion, each color class is resriced o an inerval in he Y dimension. The pixels classified o a color class are couned in a separae 94 60 grid one eighh of he our camera resoluion in each dimension. Each pixel in his color class image represens he number of occurrences of is color in a 8 8 window of he original image. While his subsampling reduces spaial resoluion, i allows for quick access o he densiy of he corresponding color in image regions. All algorihms below are performed on hese subsampled color class images, albei we use subpixel precision when possible. In he nex processing sep, simple pre-processing operaions are performed on he color images. We reduce unwaned effecs such as Bayer-paern induced orange and cyan colors nex o sharp conrass. In unreliable corner-regions of our wide-angle lens we delee all classified colors. In Fig. a, we exemplarily show he resul of classificaion for green and whie. For more deails on preprocessing we refer o [9]. The vecorizaion of lines is now implemened in wo major seps: We firs exrac he field boundary, and second, deermine he srucure of lines wihin he field boundary. The following secions describe he wo seps in deail. A. Field Boundary Exracion In robo soccer games, everyhing of ineres is locaed on he green carpe. While he area ouside he field is undefined and cluered, objecs on he field can be clearly disinguished by color and srucure. Consequenly, as a firs sep we segmen he field region, hereby furher reducing he area of ineres. We use a hree-sep boundary scanning algorihm. This algorihm firs inegraes he subsampled color-images ino a gray-level image in a manner ha i can beer represen he field region. Then, i rerieves a hisogram of field heigh in he image. In a final posprocessing sep, we smooh and fill local gaps in he hisogram. 1 Merging Color-Images: We wan o deermine he boundary of he green field. However, objecs on he field migh occlude some pars of he field. Therefore, we creae a new 94 60 gray-level image which is composed by a weighed sum of previously classified colors according o heir probabiliy of being par of he field or occluding i. Binarizaion: For a pixel o be par of he field, i mus exceed a minimum hreshold iself, be par of a largely green line or have enough field pixels below. Afer merging, we use hree hresholds pix, row and win o deermine wheher a pixel g xy is likely o be inside he field. The hreshold ess Proceedings of he 4h Workshop on Humanoid Soccer Robos A workshop of he 009 IEEE-RAS Inl. Conf. On Humanoid Robos Humanoids 009, ParisFrance, 009, December 7-10
a b c d Fig.. Visualizaion of vecorizaion process. a subsampled image of pixels classified as whie and green, wih cluered background. b skeleon inside field boundary. c all nodes wih connecions. d keynode srucure graph are arranged in order of complexiy o deal wih he obvious cases firs. Firs, we check he value of he pixel iself. If g xy pix, he pixel undergoes furher examinaion. If he pre-calculaed row-sum x {y = 1,0} g x,y+y is larger han some hreshold row, he pixel is binarized o 1. The row-sum acs here as a prior which biases weak pixels in rows wih many high-valued pixels o be par of he field. Pixels which do no pass row are examined by he mos expensive es, by examining he sum s xy of heir neighbors below in an 8 4 neighborhood and comparing s xy o win. 3 Rerieving Field Image Heigh Hisogram: Assuming ha he robo should always be locaed somewhere on he field, he field in he image always sars a he boom and reaches up o some level. This simplified view can be capured in a hisogram of image heighs. We coun consecuive binary pixels wih value 1 and 0 respecively in each column from boom-up. Once we encouner more han four consecuive pixels wih value 0, he algorihm ses he corresponding bin o be he y-coordinae of he las 1-valued pixel and proceeds o he nex column. 4 Smoohing and Gap Filling: The hisogram so far is a rough field boundary wih gaps and peaks caused by uneven illuminaions and imprecise color classificaion. We consequenly smooh he hisogram using a 1D Gaussian filer for slighly uneven bins and a median filer for small gaps and peaks. Finally, we employ a local convex corner algorihm based on [10] o only fill in he remaining gaps bu no include unwaned regions like he opponen robo s body or whie goal poss aached o he field. This algorihm simply calculaes he local convexiy: v xy = R x L x P y L y P x L x R y L y where P x is he number of he curren bin and P y is is value; L x, L y, R x and R y are he respecive values of he neighboring lef and righ bins. If v xy is 0, he op poin P y of he curren x is collinear wih is lef and righ neighbors; if v xy is posiive, he curren bin is above he line segmen beween he op poins of is lef and righ neighbors and i is below ha line segmen if v xy is negaive. The locally convex hull of he field is hen deermined by he heighs of bins wih associaed non-negaive resuls. Ieraing his scheme will evenually lead o a globally convex hull, bu for our purposes one ieraion suffices. The resul of he field boundary exracion is shown in Fig. 1 for an example image. B. Preprocessing and Skeleonizaion Wih he informaion of he field boundary, we only process he classified whie pixels inside his boundary. Then, a lowpass filer is applied o make sure ha each line cross-secion has only a single maximum-valued pixel. Skeleonizaion [1] is used o reduce he line widh o approximaely one pixel. Unlike morphological mehods which sar from he border of he line and ieraively erode i, we use a ranking operaor, which direcly finds a skeleon in he middle of a line. The operaor observes 3 3 pixel regions o decide if he cenral pixel belongs o he skeleon. Pixel having gray-level zero do no belong o he skeleon, bu o he background. For all oher pixels, he number cx, y of neighboring pixels 8-neighborhood having an equal or higher gray-level is compued and if his number is less han hree he cenral pixel is added o he skeleon. Fig. b visualizes skeleons resuling from wo soccer-field images. C. Placemen and Connecion of Nodes Nodes are placed saring a peaks of he skeleon cx, y = 0. This emphasizes crossings, which end o appear as peaks in he skeleon. Noe however, ha crossings deecion does no depend on correc node placemen a his sage. Then nodes are placed a leas wo pixels apar a pixels belonging o ridges cx, y = 1 and cx, y =. The nodes now need o be conneced o represen field lines. Firs, he connecion srucure of he skeleon is reconsruced by insering connecions where 3 3 regions of nodes overlap or ouch on he skeleon. In order o inser he few remaining connecions necessary o recover he original field lines, more global informaion of adjacen connecions is used. Lines are sreched by moving end-nodes o he las pixel of he skeleon and degree-0 nodes are spli o fill in he gaps. Finally, candidae connecions are creaed and evaluaed according o coninuiy, closure and simpliciy. Specifically, he disance Proceedings of he 4h Workshop on Humanoid Soccer Robos A workshop of he 009 IEEE-RAS Inl. Conf. On Humanoid Robos Humanoids 009, ParisFrance, 009, December 7-10
beween nodes should be small and he grayness on he line beween nodes should be similar o grayness of nodes. Furhermore, we place resricions based on he degree of nodes, ruling ou crossings of degree greaer han 4 and crossings which do no resul in coninuous lines. Examples are shown in Fig. c; we refer he ineresed reader o [1] for deails. IV. FEATURE EXTRACTION We can now easily exrac feaures such as crossings or lines from he node srucure and verify hem in he image. A. Line Crossing Deecion The node connecions produced so far are he original srucures of field lines in he image wih many deails and disorions. To exrac he key srucure, he lines are smoohed and nodes are removed a locaions of low curvaure. Shor lines ending in juncions are eliminaed and juncions ha are close ogeher and conneced are merged o form a crossing. When merging and moving nodes, we make sure ha he new nodes are placed on he skeleon o guaranee an undisored world view. The resul is shown in Fig. d. Crossing deecion here is now dramaically simplified due o he key node srucure represenaion. A degree- node wih cerain angle of edges conneced o i is an L-crossing candidae, a degree-3 node is a T-crossing candidae, and a degree-4 node is an X-crossing candidae. To verify wheher one candidae represens a real crossing, we firs use a sae machine o check ou he green-whie and whie-green color ransiion along a circle cenered a he crossing. Then, we check wheher here is a whie pah from he crossing o he nex neighbors in each direcion. Boh checks are performed in he sub-sampled color-images. B. Field Line Exracion Saring wih he fine-grained, conneced graph of observed line segmens Fig. c we can exrac field lines. Here, a field line is a conneced se of nodes wih degree wo and nodes conneced direcly o he se wih differen degree. The coordinaes of he nodes can be approximaely conneced by a sraigh line. Consequenly, we firs raverse he graph o exrac conneced componens of degree wo nodes. Because we rely on wide-angle lenses, sraigh lines in he world do no resul in sraigh lines in he image. Before proceeding, we herefore calculae undisored coordinaes of he nodes. Each componen c i is hen processed using he spli-and-merge algorihm: we fi a line l i o c i using leas squares regression [11] on he coordinaes of he nodes. The node n = arg max n ci disn, l i wih he larges disance o he fied line defines a spliing poin. We spli c i ino wo componens c 1/ i if he node-line disance is sufficienly large and recursively process he resuling componens. Componens conaining less han hree nodes are discarded. During he merging phase, we merge componens c i and c j if he parameers of l i and l j are sufficienly similar. The final field line in image coordinaes is deermined by projecing he end-poins of he componen ono he fied line. We do no use he end-poins direcly, since hese can represen par of anoher line which barely did no pass he spliing hreshold. If c i conains many nodes, is possibly wrongly mached end-poins will have limied influence on l i, resuling in a beer approximaion. Lasly, by projecing boh end-poins o he floor, we can infer he line parameers disance and angle in a egocenric coordinae frame. V. INTEGRATION OF FEATURES As described in [6], we use Mone-Carlo localizaion MCL, [1] o esimae he curren 3D pose of our soccer robos. The pose is a uple x, y, θ, where x, y denoes he posiion on he field and θ is he orienaion of he robo. The belief is updaed recursively wih: px z 1:, u 1: 1 = η pz x px x 1, u 1 px 1 z 1: 1, u 0: dx 1, 1 where η is a normalizaion consan resuling from Bayes rule, u 0: 1 is he sequence of all moion commands execued by he robo up o ime 1 and z 1: is he sequence of all observaions. The erm px x 1, u 1 is called moion model and denoes he probabiliy ha he robo ends up in sae x given i execues he moion command u 1 in sae x 1. The observaion model pz x is he likelihood of making he observaion z given he robo s curren pose is x. MCL uses a se of random samples o represen he belief of he robo abou is sae a ime. Each sample consiss of he sae vecor x i and a weighing facor ω i ha is proporional o he likelihood ha he robo is in he corresponding sae. The updae of he belief is carried ou according o he sampling imporance resampling paricle filer. Firs, he paricle saes are prediced according o he moion model. For each paricle, a new pose is drawn given he execued moion command since he previous updae. In he second sep, new individual imporance weighs are assigned o he paricles. Paricle i is weighed according o he likelihood pz x i. Finally, a new paricle se is creaed by sampling from he old se according o he paricle weighs. Each paricle survives wih a probabiliy proporional o is imporance weigh. This sep is also called resampling. In order o allow for global localizaion, e.g. in case of he kidnapped robo problem, a small amoun of he paricles is replaced by paricles wih randomly drawn poses. Addiional paricles are used if pose cerainy suddenly drops Augmened MCL, [13]. A. Crossing Observaions We rea crossing observaions similar o oher poin feaures on he field e.g., cener of goal, goal poss, marker poles. However, in conras o he oher poin feaures, crossings are no unique. To calculae he likelihood of an observaion in he paricle filer, we have o make an associaion decision: for a line crossing observaion o, each paricle i and all crossings C of he same ype X/T/L, we Proceedings of he 4h Workshop on Humanoid Soccer Robos A workshop of he 009 IEEE-RAS Inl. Conf. On Humanoid Robos Humanoids 009, ParisFrance, 009, December 7-10
mus calculae he mos likely associaion o := arg max p c x i. c C While he resul of he calculaion can be re-used in he second sep of he sampling imporance resampling, evaluaing he observaion model repeaedly is expensive and limis he number of paricles. However, we can considerably reduce he size of C by considering he egocenric orienaion of T and L-crossings. Consider, for example, a paricle a he cenerline looking owards he yellow goal and observing an L-crossing oriened owards he paricle. This paricle is quie unlikely o observe he L-crossings nex o he blue goal, which are oriened exacly opposie allocenrically. I is also unlikely o see he L-crossings nex o he yellow goal which poin owards he yellow goal. Consequenly, we spli he se L of L-crossings ino four ses L 45,..., L 315 conaining wo L-crossings of equal global orienaion each. A pre-calculaed, coarse lookup able R {45, 135, 5, 315 } L hen associaes an observaion posiion on he field and an allocenric, oriened L-crossing observaion wih he closes L- crossing. We proceed similarly wih he T-crossings, bu since he disance beween differen T crossings is large, a lookup able mapping posiions o closes T-crossings is sufficien. For X-crossings, we calculae he mos likely crossing on a per-paricle basis according o Eqn. using he observaion model. For an egocenric observaion d o, β o and an expeced egocenric posiion d i e, β e i i, we define he observaion model o be p poin o x i d i e d o exp σ d + λd o relaive o he curren paricle e β o, β i σ β 3 where σ d and σ β represen he uncerainy of a range and bearing measuremen, respecively. Noe ha he uncerainy of disance measures increases for far away objecs o compensae for he unknown pich and roll angle of our camera. Fig. 3 op righ shows he belief resuling from he observaion of a poin-landmark. B. Line Observaions In our curren sysem, we ignore lines which are shor and far away in erms of disance of he line o he origin. For each remaining line o represened by lengh of dropped perpendicular l o, disance o closes observed poin d o, and expeced angle β e, we evaluae he observaion model p line o x i d l e i, l o exp σ l + λd o e β o. β i σ β 4 Here, d, depends on he oriened disance: in conras o poin landmarks discussed above, he orienaion β o represens he angle of he observed line, no he angle of a polar coordinae. As a resul a simple observaion model which does no ake ino accoun oriened disance, would assign equal likelihood o he siuaion where he robo observes he Fig. 3. Paricle filer belief visualizaion based on observed landmarks. We used paricles on a 3D-grid and show sizes and orienaions based on he likelihood. The feaures used for localizaion are he same as in Fig. 1. Top lef: only lines, op righ: only pole, boom lef: only corners, boom righ: poles, corners and lines. line behind iself and in fron of iself, alhough he posiion of he line in fron of or behind he robo can be direcly inferred from he observaion. We herefore se in Eqn. 4 { l e l o dl e, l o = if l e, l o > 0 5 else, which eliminaes high likelihood of he unplausible siuaion. In conras o corner observaions, we canno make a disincion beween he seven long lines in our world. We use Eqn. o deermine he mos likely mach on a per-paricle basis. Noe, however, ha due o monooniciy of exp, for he arg max compuaion in Eqn. i is no necessary o evaluae he likelihood in Eqn. 5 compleely. Insead, we apply exp afer he associaion has been made and rely on he minimum argumen of exp for he associaion decision iself. In Fig. 3 op lef we visualize he belief resuling from he observaion of he wo lines in Fig. 1. C. Combined Observaion Model For each observaion o j, we ensure ha is observaion likelihood is larger han some uniform hreshold. We furher incorporae confidence values c j from our vision sysem such ha unconfiden observaions o j have less influence on he final disribuion han confiden observaions in he same frame: p o j x i = α uni p uni o j x i + α normal p o j x i where α uni = α base +1 α base 1 c j and α base ]0, 1[ is a uniform floor. We furher se α uni + α normal = 1 and p uni o j x i o be he Lebesgue measure of he observaion range. Assuming independence of observaions, as ypically done in MCL, he observaion likelihood of a paricle hen amouns o he produc of all single observaions x i p comb z p line l x i p poin o x i, l L o P 6, Proceedings of he 4h Workshop on Humanoid Soccer Robos A workshop of he 009 IEEE-RAS Inl. Conf. On Humanoid Robos Humanoids 009, ParisFrance, 009, December 7-10
Fracion of Recorded Poses 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 Wih lines Wihou lines Ground-Truh Comparison 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 Disance o Ground Truh Fig. 4. Fracion of frames which are closer o ground ruh han some hreshold meers. The esimaed poses were recorded by a remoe-conrolled robo, once wih line and crossing-deecion enabled and once wihou abou 9000 poses each. Ground ruh was deermined using an Opirack moion capure sysem and markers aached o he robo s head. where P includes corners and oher poin landmarks such as goal ceners and poles marking he end of he cener line. The combined belief resuling from observaions of poin and line landmarks is shown in Fig. 3 boom righ. VI. RESULTS Our 1.3 GHz sysem runs a abou 4 frames per second using beween 50 and 1000 paricles depending on he cerainy of he curren pose. Boh KidSize and TeenSize robos profi enormously from line-based localizaion. Consider he pose cerainy of he robo in our running example. We illusrae he beliefs in Fig. 3 by disribuing many paricles in a regular 3D-grid on he field. Besides lines and corners, he robo only observes a pole a he side of he field. Wih color-based localizaion only, he posiion on he field is no a all clear from he image. Using only corners, he belief is reduced o wo posiions. The only colored landmark observed is hen enough o furher reduce he pose belief o an almos unimodal disribuion. For a given frame, we run a paricle filer updae and selec he mos likely orienaion z for each planar posiion p xy. We hen show his paricle sized in proporion o is likelihood a posiion x, y. To furher quanify he performance of our algorihm we le a robo walk for abou 5 minues across he field using remoeconrol. In addiion o esimaed poses we record ground ruh posiions using an Opirack moion capure sysem and infrared-reflecive markers aached o he robo s head. The experimen was performed wice, once using line and crossing deecion and once wihou, wih similar rajecories. Boh rajecories conain abou 9000 poses. We hen deermined he percenage of recorded frames for which he disance beween he robo s esimaed pose o ground ruh was less han some hreshold. The resul is depiced in Fig. 4. Noe ha wihou lines only 87% of he recorded poses are wihin 40 cm of he ground ruh while wih line and crossing deecion enabled 99% are in his range. In he TeenSize league, robos play on a field of he same size as he KidSize field, bu he robos are by definiion much larger. The srucural informaion which is visible from he perspecive of a TeenSize robo is consequenly much more informaive. Our TeenSize robo Dynaped, he champion of he Graz 009 world cup herefore could mainly rely on allocenric informaion from he paricle filer for is decisions insead of previously used egocenric informaion. VII. CONCLUSION In his work, we inroduced a line-deecion mehod based on mehods developed for he idenificaion of srucure in handwrien digis. We firs described how o find he boundary of he soccer field. Whie poins wihin his region are hen skeleonized and a simple graph srucure is rerieved from he skeleon. The graph srucure has advanageous properies: field-line corner candidaes are represened by nodes and field-lines are represened by edges. This graph srucure is hen used o verify linear componens and crossings and o deermine heir parameers. Due o he graph represenaion, clusering or averaging of noisy locally esimaed line parameers can be avoided. Finally, we showed how lines and crossings can be used in Mone-Carlo localizaion. The paper describes observaion models and opimizaions o speed up associaion decisions. Our observaion models were exemplarily demonsraed using visualizaions of resuling paricle filer beliefs. Evaluaion of our localizaion on he real robo showed small smaller differences o ground ruh when lines and corners were used. The algorihms described were used on our KidSize and winning TeenSize soccer robos during RoboCup 009. Acknowledgemens: This projec is suppored by he German Research Foundaion DFG, gran BE556/- and BE556/4. REFERENCES [1] S. Behnke, M. Pfiser, and R. Rojas, Recogniion of handwrien digis using srucural informaion, in Proc. of ICNN, 1997. [] N. Henderson, P. Nicklin, A. Wong, J. Kulk, K. Chalup, R. King, H. Middleon, S. Tang, and A. Buckley, The 008 NUManoids Team Repor. [3] M. Sridharan and P. Sone, Real-ime vision on a mobile robo plaform, in 005 IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems, 005.IROS 005, 005, pp. 148 153. [4] T. Rofer and M. Jungel, Fas and robus edge-based localizaion in he sony four-legged robo league, Lecure Noes in Compuer Science, vol. 300, pp. 6 73, 004. [5] A. Bais, R. Sablanig, and G. 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